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Graphs in Perturbation Theory

Graphs in Perturbation Theory
Author: Michael Borinsky
Publisher: Springer
Total Pages: 173
Release: 2018-11-04
Genre: Science
ISBN: 3030035417

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This book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.


Graphs in Perturbation Theory

Graphs in Perturbation Theory
Author: Michael Borinsky
Publisher:
Total Pages:
Release: 2018
Genre: Algebra
ISBN:

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Large-Order Behaviour of Perturbation Theory

Large-Order Behaviour of Perturbation Theory
Author: J.C. Le Guillou
Publisher: Elsevier
Total Pages: 595
Release: 2012-12-02
Genre: Mathematics
ISBN: 0444596208

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This volume is concerned with the determination of the behaviour of perturbation theory at large orders in quantum mechanics and quantum field theory, and its application to the problem of summation of perturbation series. Perturbation series in quantum field theory and in many quantum mechanics models are only asymptotic and thus diverge for all values of the expansion parameter. Their behaviour at large orders provides information about whether they define the theory uniquely (the problem of Borel summability). It suggests methods to extract numerical information from the series when the expansion parameter is not small. The articles reprinted here deal with the explicit evaluation of large-order behaviour in many quantum mechanics and field theory models. The large-order behaviour is related to barrier penetration effects for unphysical values of the expansion parameter, which can be calculated by WKB or instanton methods. The calculation of critical exponents of &fgr;4 field theory is presented as a practical application.


Perturbation theory for linear operators

Perturbation theory for linear operators
Author: Tosio Kato
Publisher: Springer Science & Business Media
Total Pages: 610
Release: 2013-06-29
Genre: Mathematics
ISBN: 3662126788

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Mathematical Foundations and Applications of Graph Entropy

Mathematical Foundations and Applications of Graph Entropy
Author: Matthias Dehmer
Publisher: John Wiley & Sons
Total Pages: 298
Release: 2017-09-12
Genre: Medical
ISBN: 3527339094

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This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory. An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-life areas. Filling a gap in the contemporary literature this is an invaluable reference for a number of disciplines, including mathematicians, computer scientists, computational biologists, and structural chemists.


Drawing Theories Apart

Drawing Theories Apart
Author: David Kaiser
Publisher: University of Chicago Press
Total Pages: 376
Release: 2009-11-15
Genre: Science
ISBN: 0226422658

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Winner of the 2007 Pfizer Prize from the History of Science Society. Feynman diagrams have revolutionized nearly every aspect of theoretical physics since the middle of the twentieth century. Introduced by the American physicist Richard Feynman (1918-88) soon after World War II as a means of simplifying lengthy calculations in quantum electrodynamics, they soon gained adherents in many branches of the discipline. Yet as new physicists adopted the tiny line drawings, they also adapted the diagrams and introduced their own interpretations. Drawing Theories Apart traces how generations of young theorists learned to frame their research in terms of the diagrams—and how both the diagrams and their users were molded in the process. Drawing on rich archival materials, interviews, and more than five hundred scientific articles from the period, Drawing Theories Apart uses the Feynman diagrams as a means to explore the development of American postwar physics. By focusing on the ways young physicists learned new calculational skills, David Kaiser frames his story around the crafting and stabilizing of the basic tools in the physicist's kit—thus offering the first book to follow the diagrams once they left Feynman's hands and entered the physics vernacular.


Handbook of Graph Theory

Handbook of Graph Theory
Author: Jonathan L. Gross
Publisher: CRC Press
Total Pages: 1200
Release: 2003-12-29
Genre: Computers
ISBN: 9780203490204

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The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approach


Data Privacy Management, Cryptocurrencies and Blockchain Technology

Data Privacy Management, Cryptocurrencies and Blockchain Technology
Author: Cristina Pérez-Solà
Publisher: Springer Nature
Total Pages: 404
Release: 2019-09-20
Genre: Computers
ISBN: 3030315002

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This book constitutes the refereed conference proceedings of the 14th International Workshop on Data Privacy Management, DPM 2019, and the Third International Workshop on Cryptocurrencies and Blockchain Technology, CBT 2019, held in conjunction with the 24th European Symposium on Research in Computer Security, ESORICS 2019, held in Luxembourg in September 2019. For the CBT Workshop 10 full and 8 short papers were accepted out of 39 submissions. The selected papers are organized in the following topical headings: lightning networks and level 2; smart contracts and applications; and payment systems, privacy and mining. The DPM Workshop received 26 submissions from which 8 full and 2 short papers were selected for presentation. The papers focus on privacy preserving data analysis; field/lab studies; and privacy by design and data anonymization. Chapter 2, “Integral Privacy Compliant Statistics Computation,” and Chapter 8, “Graph Perturbation as Noise Graph Addition: a New Perspective for Graph Anonymization,” of this book are available open access under a CC BY 4.0 license at link.springer.com.